An efficient operational matrix approach for the solutions of Burgers' and fractional Burgers' equations using wavelets

In this paper, we have developed an efficient Chebyshev wavelet-Picard method for solving Burgers’ equation and time-fractional Burgers’ equation. In order to get the solution, we decompose the nonlinear PDE by Picard method and then convert into a system of algebraic equations. Convergence analysis of the proposed wavelet method is also discussed. The proposed wavelet solutions are compared with the solutions obtained by Cole-Hopf transformation and Haar wavelet method. Satisfactory agreement with HAM and analytical solution is observed. Some illustrative examples are given to demonstrate the efficiency and accuracy of the proposed wavelet method.